A computer virus is self-replicating software that spreads by inserting copies of itself into other software. In a way, a computer virus is similar to a human virus in that it spreads through infection and relies on a host. Some viruses can be intentionally destructive (for example, by destroying data) whereas others are created simply to annoy a computer user.
Yes, Viruses essentially send themselves around and include the code necessary to reproduce as part of their contents. Spyware however is reproduced through web content (such as downloads) or other programs that users run on their machines (usually without their knowledge or consent).
Your computer can become infected by a computer virus in a variety of ways:
The only way you can really know if your computer is infected by a virus, is by scanning your machine with an up-to-date anti-virus program. It will tell you what virus your machine is infected with and tell you what steps to take to remove it.